輸出WRT網絡權的持有另一個輸出恆定

Question

梯度

假設我有一個簡單的MLP

而且我有一些損失函數的梯度相對於輸出層得到g^= [0，-1]（也就是增加第二個輸出變量減少損失函數）。

如果我根據我的網絡參數獲得G的梯度並應用梯度體面權重更新，那麼第二個輸出變量應該增加，但對第一個輸出變量沒有任何說法，梯度的縮放應用幾乎肯定會改變輸出變量（是增加還是減少）

如何修改我的損失函數或任何梯度計算以確保第一個輸出不會更改？

Answer 1

更新：我誤解了這個問題。這是新的答案。

爲此，您需要僅更新隱藏層和第二個輸出單元之間的連接，同時保持隱藏層和第一個輸出單元之間的連接完好。

第一種方法是引入兩組變量：一個用於隱藏層和第一個輸出單元之間的連接，其餘一個用於連接。然後您可以使用tf.stack將它們組合起來，並通過var_list以獲得相應的衍生產品。這就像（僅用於演示未測試小心使用。）：

out1 = tf.matmul(hidden, W_h_to_out1) + b_h_to_out1 
out2 = tf.matmul(hidden, W_h_to_out2) + b_h_to_out2 
out = tf.stack([out1, out2]) 
out = tf.transpose(tf.reshape(out, [2, -1])) 
loss = some_function_of(out) 
optimizer = tf.train.GradientDescentOptimizer(0.1) 
train_op_second_unit = optimizer.minimize(loss, var_list=[W_h_to_out2, b_h_to_out2]) 

另一種方法是使用口罩。當你使用一些框架（比如纖細，Keras等）時，這更容易實現，並且更靈活，我會以這種方式推薦。將第一個輸出單元隱藏到丟失功能的想法，同時不改變第二個輸出單元。 這可以通過使用二進制變量完成：如果要保留它，請將乘以1，然後乘以0將其刪除。下面的代碼：

import tensorflow as tf 
import numpy as np 

# let's make our tiny dataset: (x, y) pairs, where x = (x1, x2, x3), y = (y1, y2), 
# and y1 = x1+x2+x3, y2 = x1^2+x2^2+x3^2 

# n_sample data points 
n_sample = 8 
data_x = np.random.random((n_sample, 3)) 
data_y = np.zeros((n_sample, 2)) 
data_y[:, 0] += np.sum(data_x, axis=1) 
data_y[:, 1] += np.sum(data_x**2, axis=1) 
data_y += 0.01 * np.random.random((n_sample, 2)) # add some noise 


# build graph 
# suppose we have a network of shape [3, 4, 2], i.e.: one hidden layer of size 4. 

x = tf.placeholder(tf.float32, shape=[None, 3], name='x') 
y = tf.placeholder(tf.float32, shape=[None, 2], name='y') 
mask = tf.placeholder(tf.float32, shape=[None, 2], name='mask') 

W1 = tf.Variable(tf.random_normal(shape=[3, 4], stddev=0.1), name='W1') 
b1 = tf.Variable(tf.random_normal(shape=[4], stddev=0.1), name='b1') 
hidden = tf.nn.sigmoid(tf.matmul(x, W1) + b1) 
W2 = tf.Variable(tf.random_normal(shape=[4, 2], stddev=0.1), name='W2') 
b2 = tf.Variable(tf.random_normal(shape=[2], stddev=0.1), name='b2') 
out = tf.matmul(hidden, W2) + b2 
loss = tf.reduce_mean(tf.square(out - y)) 

# multiply out by mask, thus out[0] is "invisible" to loss, and its gradient will not be propagated 
masked_out = mask * out 
loss2 = tf.reduce_mean(tf.square(masked_out - y)) 

optimizer = tf.train.GradientDescentOptimizer(0.1) 
train_op_all = optimizer.minimize(loss) # update all variables in the network 
train_op12 = optimizer.minimize(loss, var_list=[W2, b2]) # update hidden -> output layer 
train_op2 = optimizer.minimize(loss2, var_list=[W2, b2]) # update hidden -> second output unit 


sess = tf.InteractiveSession() 
sess.run(tf.global_variables_initializer()) 
mask_out1 = np.zeros((n_sample, 2)) 
mask_out1[:, 1] += 1.0 
# print(mask_out1) 
print(sess.run([hidden, out, loss, loss2], feed_dict={x: data_x, y: data_y, mask: mask_out1})) 

# In this case, only out2 is updated. You see the loss and loss2 decreases. 
sess.run(train_op2, feed_dict={x: data_x, y:data_y, mask: mask_out1}) 
print(sess.run([hidden, out, loss, loss2], feed_dict={x: data_x, y:data_y, mask: mask_out1})) 

# In this case, both out1 and out2 is updated. You see the loss and loss2 decreases. 
sess.run(train_op12, feed_dict={x: data_x, y:data_y, mask: mask_out1}) 
print(sess.run([hidden, out, loss, loss2], feed_dict={x: data_x, y:data_y, mask: mask_out1})) 

# In this case, everything is updated. You see the loss and loss2 decreases. 
sess.run(train_op_all, feed_dict={x: data_x, y:data_y, mask: mask_out1}) 
print(sess.run([hidden, out, loss, loss2], feed_dict={x: data_x, y:data_y, mask: mask_out1})) 
sess.close() 

=======================下面是舊的答案========== ====================

要得到衍生產品wrt不同的變量，你可以通過一個var_list來決定更新哪個變量。下面是一個例子：

import tensorflow as tf 
import numpy as np 

# let's make our tiny dataset: (x, y) pairs, where x = (x1, x2, x3), y = (y1, y2), 
# and y1 = x1+x2+x3, y2 = x1^2+x2^2+x3^2 

# n_sample data points 
n_sample = 8 
data_x = np.random.random((n_sample, 3)) 
data_y = np.zeros((n_sample, 2)) 
data_y[:, 0] += np.sum(data_x, axis=1) 
data_y[:, 1] += np.sum(data_x**2, axis=1) 
data_y += 0.01 * np.random.random((n_sample, 2)) # add some noise 


# build graph 
# suppose we have a network of shape [3, 4, 2], i.e.: one hidden layer of size 4. 

x = tf.placeholder(tf.float32, shape=[None, 3], name='x') 
y = tf.placeholder(tf.float32, shape=[None, 2], name='y') 

W1 = tf.Variable(tf.random_normal(shape=[3, 4], stddev=0.1), name='W1') 
b1 = tf.Variable(tf.random_normal(shape=[4], stddev=0.1), name='b1') 
hidden = tf.nn.sigmoid(tf.matmul(x, W1) + b1) 
W2 = tf.Variable(tf.random_normal(shape=[4, 2], stddev=0.1), name='W2') 
b2 = tf.Variable(tf.random_normal(shape=[2], stddev=0.1), name='b2') 
out = tf.matmul(hidden, W2) + b2 

loss = tf.reduce_mean(tf.square(out - y)) 
optimizer = tf.train.GradientDescentOptimizer(0.1) 
# You can pass a variable list to decide which variable(s) to minimize. 
train_op_second_layer = optimizer.minimize(loss, var_list=[W2, b2]) 
# If there is no var_list, all variables will be updated. 
train_op_all = optimizer.minimize(loss) 

sess = tf.InteractiveSession() 
sess.run(tf.global_variables_initializer()) 
print(sess.run([W1, b1, W2, b2, loss], feed_dict={x: data_x, y:data_y})) 

# In this case, only W2 and b2 are updated. You see the loss decreases. 
sess.run(train_op_second_layer, feed_dict={x: data_x, y:data_y}) 
print(sess.run([W1, b1, W2, b2, loss], feed_dict={x: data_x, y:data_y})) 

# In this case, all variables are updated. You see the loss decreases. 
sess.run(train_op_all, feed_dict={x: data_x, y:data_y}) 
print(sess.run([W1, b1, W2, b2, loss], feed_dict={x: data_x, y:data_y})) 
sess.close()